A team of researchers at the University of Electronic Science and Technology of China in Chengdu has now tackled one of the most stubborn demands in this field: guaranteeing not just that a hydraulic actuator eventually tracks its commanded trajectory, but that the tracking error shrinks to a small neighborhood of zero within a deadline chosen in advance by the designer. In a study published in Applied Intelligence, Chen Wang, Jinping Ye, Xin Chen, Zhenlei Chen, Dan Jiang, Qing Guo and colleagues present a predefined-time adaptive neural backstepping controller for electro-hydraulic actuator systems, or EHASs, that remains stable even when key hydraulic parameters are uncertain and unknown external loads push against the piston.

The distinction between eventually and on time matters more than it might first appear. Conventional adaptive and backstepping controllers, which have dominated the hydraulic control literature for years, typically guarantee asymptotic convergence: the error decays toward zero as time stretches toward infinity, with no firm promise about when it becomes small enough to matter. Finite-time and fixed-time controllers tightened that promise, guaranteeing convergence within a bound that depends on initial conditions or on system parameters. Predefined-time control goes further still. The settling bound is set directly by the designer, independent of where the system starts, so an engineer can specify, for example, that the actuator must lock onto its target within two seconds regardless of how far away it begins. That kind of hard deadline is exactly what safety-critical and high-throughput applications demand.

The central obstacle is uncertainty. In an electro-hydraulic actuator, the dynamics involve hydraulic natural frequencies, leakage coefficients, effective bulk moduli and friction characteristics that are difficult to measure precisely and that drift over the machine’s life. The Chengdu team’s approach begins by gathering these unknown parameters into two lumped nonlinear terms rather than trying to estimate each one separately. Those lumped terms are then approximated online by radial basis function neural networks, a class of neural networks well suited to control because their outputs are linear in their weights. This linearity lets the adaptation law adjust the network weights in real time using Lyapunov-based arguments, the standard mathematical machinery for proving that a controlled system’s energy-like quantity decreases and the state converges.

A subtler mathematical hazard lurks in predefined-time designs for hydraulic systems. The error surfaces used in these schemes often contain low-order fractional-power terms, expressions in which the tracking error is raised to a power less than one. Near zero error, the derivatives of such terms can blow up, producing singularities in the virtual controllers that the backstepping procedure computes at each step of the design. A controller that demands infinite effort at the very moment the system approaches its goal is obviously unusable. The researchers resolved this by introducing twice continuously differentiable segmented functions that regularize the fractional-power terms, smoothing the expressions near the origin so the virtual controllers remain finite and well defined while preserving the predefined-time convergence property away from the origin.

With these ingredients in place, the team carried out a rigorous theoretical analysis establishing what control theorists call practical predefined-time stability. In practical stability, the error is not promised to reach exactly zero but to enter an adjustable neighborhood of zero, a small residual region whose size the designer can tune. The analysis proves that both the tracking error and the errors in the adaptive parameter estimates converge into that tunable neighborhood within the designer-specified time. This is a meaningful guarantee: it means the deadline is not an empirical observation from simulations but a mathematical property of the closed-loop system, derived under explicit assumptions about the uncertainty bounds.

The practical stakes become clear when one considers where electro-hydraulic actuators must perform on schedule. In a leg exoskeleton driven by hydraulics, a joint that lags its commanded trajectory by even a fraction of a second can destabilize a walking gait. In flight-control actuation, deadline violations translate directly into degraded handling. In industrial automation, cycle-time guarantees determine throughput. Earlier work in the field, including adaptive backstepping sliding-mode schemes for hydraulic manipulators, high-gain extended-state-observer controllers for position tracking, and barrier Lyapunov function methods for prescribed performance, steadily improved transient and steady-state accuracy, but none of these approaches could guarantee convergence within a time fixed by the designer in the presence of the full combination of parameter uncertainty and unknown loads.

The fixed-time and predefined-time literature that inspired the new work has matured rapidly in other domains. Researchers have applied fixed-time adaptive fuzzy and neural control to spacecraft attitude tracking, vehicle suspensions, flexible-joint manipulators, robotic manipulator fault tolerance and multi-UAV formation control. Polyakov’s foundational 2012 work on fixed-time stabilization of linear systems opened the door, and subsequent designs extended the idea to nonlinear and uncertain systems. What the Chengdu team contributes is the careful translation of these ideas to the specific, messy setting of hydraulic actuation, where the nonlinear flow-pressure characteristics, unmatched uncertainties and singularity risks of fractional-power terms make the mathematics considerably harder than in the electrical and aerospace systems where predefined-time control was first demonstrated.

Validation came in two stages. Simulation studies first confirmed that the theoretical convergence bounds hold in the idealized model, with the tracking error and the neural network’s weight-estimation errors settling into their prescribed neighborhoods within the specified time. The team then ran comparative experiments against both finite-time controllers and conventional backstepping controllers on an electro-hydraulic actuator setup. The results showed measurably improved tracking accuracy over both benchmarks, with the new controller reaching its small-error neighborhood faster and holding it more tightly under the same uncertain conditions. The comparisons matter because they isolate the benefit of the predefined-time formulation: the same underlying plant, the same class of disturbances, but a controller whose convergence deadline is a design parameter rather than an emergent property.

The work, published as volume 56, article 488 of Applied Intelligence with support from China’s national Brain Science and Brain-like Intelligence Technology major project and provincial science programs, points toward hydraulic machines that can be certified against timing guarantees rather than merely tuned until they behave. Because the neural networks learn the lumped uncertainties online, the approach does not require an accurate hydraulic model to be measured in advance, and because the settling time is chosen by the designer, the same controller can be retargeted to faster or slower tasks by adjusting a parameter rather than redesigning the control law. For the factories, aircraft and legged robots that depend on fluid power, the study offers a step toward actuators whose punctuality is written into the mathematics rather than hoped for in the field.

Subject of Research: Predefined-time adaptive neural control of electro-hydraulic actuator systems with parameter uncertainties

Article Title: Predefined-time adaptive neural control for electro-hydraulic actuator systems with parameter uncertainties

Article References: Wang, C., Ye, J., Chen, X., Chen, Z., Jiang, D., & Guo, Q. (2026). Predefined-time adaptive neural control for electro-hydraulic actuator systems with parameter uncertainties. Applied Intelligence, 56(15), Article 488. https://doi.org/10.1007/s10489-026-07535-0

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07535-0

Keywords: electro-hydraulic actuators, predefined-time control, adaptive control, neural networks, backstepping control, radial basis function neural networks, parameter uncertainties, tracking error convergence, practical stability, industrial automation, hydraulic systems, control theory

The central challenge the researchers tackled is a fundamental tension in flight control. On one hand, engineers want to guarantee that the aircraft’s tracking errors stay within strict bounds, a property known as prescribed performance, so that the jet never strays outside a safe corridor during its descent. On the other hand, the aircraft’s control surfaces and engine thrust are physically limited. When a controller demands more deflection or thrust than the actuators can deliver, a condition called actuator saturation, the aircraft temporarily stops obeying commands and the error can breach the very boundaries the performance function was designed to enforce. Once those boundaries are violated, many prescribed performance controllers fail catastrophically, because their mathematics assumes the error always remains inside a constrained domain.

The Harbin team’s solution is elegantly pragmatic: rather than pretending saturation will never happen, they built a controller that bends without breaking. At the heart of the method lies a predefined-time prescribed performance function, a mathematical curve that dictates how quickly and how tightly the landing error must shrink. Unlike conventional exponential convergence guarantees, which depend on initial conditions, a predefined-time guarantee ensures the error converges within a time chosen by the designer, no matter where the aircraft starts. This is a significant advantage in carrier operations, where the approach window is short and unforgiving and where an autopilot that converges ‘eventually’ is not good enough.

To work with these constraints mathematically, the researchers employed an error transformation technique that converts the constrained error domain into an equivalent unconstrained one. In essence, the transformation warps the coordinate system so that as long as the transformed error remains bounded, the physical landing error is guaranteed to stay inside its prescribed funnel. This allows standard control design tools to be applied to a problem that would otherwise involve hard, nonlinear boundaries. The transformed error then feeds into a nonsingular fast terminal integral sliding mode controller, a robust control strategy renowned for its ability to reject external disturbances. The ‘terminal’ component drives errors to zero in finite time rather than merely asymptotically, while the ‘nonsingular’ design avoids the mathematical pitfalls, such as division by zero, that plague naive terminal sliding mode formulations.

The truly novel ingredient, however, is the flexible adjustment mechanism embedded within the performance function itself. When the controller detects that actuators are saturating, meaning the aircraft cannot fully execute the commanded deflections, the mechanism adaptively relaxes the local performance boundaries, giving the aircraft room to recover rather than demanding the impossible. Once the saturation episode passes, the boundaries tighten again, and the landing proceeds with its original accuracy targets intact. This adaptive flexibility prevents the boundary violations that would otherwise cause the error transformation to blow up and the controller to fail. Complementing this mechanism, the team designed an auxiliary system that maintains stability during saturation events, a well-known strategy in the control literature that the authors integrated carefully with their performance framework.

Disturbance rejection receives equally thorough treatment. The turbulent airwake behind a carrier’s island superstructure is modeled in the study as a set of external disturbances acting on the aircraft’s translational and rotational dynamics, with components that vary sinusoidally over time to mimic the chaotic flow field. To counter these, the researchers developed a predefined-time disturbance observer, an algorithm that estimates the unknown disturbance signals and feeds the estimates directly into the control law as compensation. Because the observer converges in predefined time, the compensation kicks in quickly enough to matter during the brief final approach. The team also introduced a predefined-time reference model to generate the command signals that the inner control loops track. This choice eliminates a chronic computational problem in conventional backstepping control designs, where repeated differentiation of command signals leads to ‘explosion of complexity,’ an exponential growth in the analytic terms that must be computed at each step.

The aircraft model used in the study is a full six-degree-of-freedom representation of a carrier-based aircraft, complete with the coupling between roll, pitch, and yaw dynamics that arises from the aircraft’s inertia properties, aerodynamic coefficients for lift, drag, and side force, and the contributions of the elevator, aileron, rudder, and direct lift flap. The guidance problem is framed as following a moving deck landing path, with the controller tasked with tracking the ship’s motion while respecting output constraints on altitude and attitude errors. This comprehensive modeling matters, because simplified models often hide exactly the coupling effects that make real carrier approaches so treacherous, particularly the way lateral gusts induce rolling moments that must be countered within fractions of a second.

To benchmark their approach, the authors compared FPTPPC against three competing strategies in simulation: dynamic inverse control, a classical technique that cancels the aircraft’s nonlinearities through model inversion; predefined-time control without prescribed performance; and standard prescribed performance control without the flexible saturation mechanism. The results showed that the proposed method reduced path following errors and improved overall landing accuracy relative to all three baselines. The simulations also demonstrated that the flexible adjustment mechanism kept the controller stable and accurate through saturation events that would have destabilized a rigid prescribed performance design. While the study is computational rather than flight-tested, the consistency of the improvements across the comparison set lends weight to the practical promise of the approach.

The implications extend beyond naval aviation. The core ideas, predefined-time convergence guarantees, flexible performance boundaries that tolerate actuator limits, and disturbance observers that compensate within a designer-chosen horizon, are directly transferable to other safety-critical control problems, including spacecraft attitude control, unmanned aerial vehicle operations in gusty conditions, and robotic systems with limited actuator authority. Related work in the same journal and elsewhere has begun applying predefined-time and anti-saturation techniques to fault-tolerant flight control, suggesting a broader research movement toward controllers that are honest about physical limits rather than assuming them away. For the moment, the Harbin team’s contribution stands as a careful piece of control engineering: a mathematically rigorous answer to the question of what an autopilot should do when the ideal command and the possible command diverge, at the worst possible moment, a few hundred feet above a moving flight deck.

Subject of Research: Automatic carrier landing control using flexible predefined-time prescribed performance control under output constraints, actuator saturation, and airwake disturbances

Article Title: Flexible Predefined-Time Prescribed Performance Control for Automatic Carrier Landing with Output Constraints and Actuator Saturation

Article References: Wang, Z., Zhu, Q., Kong, L., & Wang, L. (2026). Flexible Predefined-Time Prescribed Performance Control for Automatic Carrier Landing with Output Constraints and Actuator Saturation. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01239-y

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01239-y

Keywords: automatic carrier landing, prescribed performance control, predefined-time control, actuator saturation, sliding mode control, airwake disturbance, flight control systems, disturbance observer, carrier-based aircraft, nonlinear control, landing accuracy, Harbin Engineering University

The research, published in the International Journal of Aeronautical and Space Sciences by Qilong Wu of Huainan Normal University, Qidan Zhu of Harbin Engineering University, and their colleagues, including Lunpan Wei, Lipeng Wang, and Wenqiang Jiang of the China Ship Development and Design Center, tackles a problem that has long frustrated engineers: how to guarantee that a landing aircraft stays on its glide path within a strictly bounded error, and that it does so within a time window chosen in advance by the designer, regardless of where the aircraft starts its approach. The work was supported by the National Natural Science Foundation of China and other national and provincial funding bodies.

At the heart of the new scheme is what the authors call a predefined-time prescribed performance function, or PTPPF. Prescribed performance control is a technique that constrains the tracking error, the difference between where the aircraft should be and where it actually is, to remain inside a shrinking envelope. Think of it as a funnel around the ideal glide slope: the aircraft’s deviation is mathematically forbidden from escaping the funnel walls, and the funnel narrows as the aircraft nears the deck. What makes the new formulation distinctive is the predefined-time element. In many conventional designs, the convergence of the error depends on the initial conditions, meaning a jet that starts its approach far from the ideal path may take an unpredictable amount of time to settle. The PTPPF removes that dependency entirely, guaranteeing that the error converges within a time set by the control engineer before the mission even begins.

Guaranteeing a bounded error is only half the battle, however. The second pillar of the approach is a predefined-time sliding mode controller, or PTSMC. Sliding mode control is a well-established robust technique that drives a system’s state onto a chosen sliding surface and then forces it to slide along that surface toward the target, effectively ignoring matched uncertainties and external disturbances along the way. Its weakness has traditionally been the chattering phenomenon, in which the control signal oscillates rapidly, and the fact that classical finite-time versions offer convergence speeds that vary with initial conditions. The predefined-time variant designed by the team enhances robustness against the nonlinear uncertainties and external disturbances that plague carrier approaches, while ensuring that the sliding dynamics complete their work within the designer’s chosen deadline.

The third and perhaps most ingenious component is a prescribed-time extended state observer, or PTESO. Extended state observers are devices that treat all the unknown disturbances acting on a system, including unmodeled dynamics, wind gusts, and even actuator faults, as an additional augmented state to be estimated alongside the system’s physical states. Once estimated, these lumped disturbances can be cancelled out in real time within the control loop, a strategy known as active disturbance rejection. The prescribed-time version developed here goes further: it promises that its estimates of the combined disturbances and actuator faults become accurate within a prescribed time, allowing the controller to compensate for a failing elevator or a sudden shift in the ship’s turbulent wake almost as soon as it occurs, rather than gradually over the course of the approach.

To prove that this elaborate architecture is safe rather than merely plausible, the authors carried out a Lyapunov-based stability analysis. Lyapunov methods are the gold standard of nonlinear control theory: the designer constructs an energy-like function of the closed-loop system and demonstrates mathematically that this function decreases along the system’s trajectories, which implies that all signals remain bounded and that the tracking error behaves as intended. In this case, the analysis establishes two critical guarantees simultaneously: every closed-loop signal stays bounded, and the tracking error converges within the predefined time, no matter the initial conditions. That combination of boundedness and deadline-driven convergence is what separates this work from earlier prescribed performance designs, which typically offered only asymptotic or condition-dependent convergence.

The true test of any carrier landing control law comes in simulation that faithfully reproduces the hostile environment of a moving flight deck. The team’s carrier landing experiments incorporated three of the most punishing factors at once: the carrier air-wake, the turbulent and horizontally offset airflow generated by the ship’s island superstructure as it washes over the approaching aircraft; the deck motion, meaning the heave, pitch, and roll of the landing point as the ship responds to waves; and actuator faults, including partial loss of control effectiveness. These are precisely the coupled hazards that have caused past approaches to degrade, because a controller tuned for calm conditions can be overwhelmed when disturbances and hardware failures arrive together.

The results, according to the authors, show that the proposed method significantly improves transient performance, disturbance rejection, and landing accuracy compared with existing techniques. Transient performance matters enormously in this context: the moments right after the aircraft enters the glide path, or right after a fault occurs, are when deviations are largest and most dangerous. By confining the error inside the prescribed performance funnel from the very start and compensating disturbances through the observer in real time, the scheme keeps those dangerous excursions small and short-lived. The practical implication is a tighter, more predictable touchdown point on the deck, which translates directly into reduced structural stress on the airframe and lower risk of missing the arresting wires.

The significance of the predefined-time formulation becomes clearer when one considers the communication environment referenced in the study’s title. Carrier-based aircraft operate in data links with the ship, and guidance updates may arrive late or intermittently. A control law whose convergence time balloons when conditions are unfavorable offers no firm promise to the pilot or the mission planner. By contrast, a scheme in which the error is guaranteed to converge within a time fixed at design stage, independent of initial conditions, allows the entire approach to be choreographed against a known clock, which is essential when the landing window is dictated by the ship’s motion and the recovery schedule of the air wing.

The work also fits into a broader and rapidly accelerating research trend. Fixed-time and predefined-time control methods have recently swept through the control theory literature, with applications demonstrated for multiagent consensus, microgrid frequency regulation, hypersonic vehicles, spacecraft attitude stabilization, and quadrotor drones, including vehicles suffering actuator failures. Meanwhile, extended state observers have been combined with sliding mode and super-twisting techniques for carrier landing in a series of recent studies, and fault-tolerant control for carrier-based aircraft has evolved from fault reconstruction schemes to adaptive neural approaches. The new paper synthesizes these strands, wrapping a predefined-time prescribed performance function, a predefined-time sliding mode controller, and a prescribed-time extended state observer into a single fault-tolerant architecture with formal stability proofs.

For now, the results rest on simulation experiments rather than flight tests, and the authors note that the underlying code is not publicly available due to project confidentiality and institutional restrictions, though it can be requested from the corresponding author for academic purposes. The data supporting the findings are likewise available upon reasonable request with laboratory approval. Those caveats are standard for research at this stage, and the gap between simulated and real carrier operations remains a formidable one, involving sensor noise, actuator saturation limits, and the sheer unpredictability of the maritime environment. Nevertheless, the mathematical guarantees established in the paper, bounded closed-loop signals and deadline-driven error convergence under simultaneous air-wake disturbance, deck motion, and actuator faults, represent a meaningful step toward the long-sought goal of fully autonomous, fault-resilient carrier recoveries. If future flight validation confirms the simulation results, the technology could one day allow unmanned carrier-based aircraft, and perhaps crewed ones, to come aboard in conditions that today demand the finest human piloting skills in existence.

Subject of Research: Fault-tolerant predefined-time control for automatic aircraft carrier landing under air-wake disturbances and actuator faults

Article Title: Robust Predefined-Time Fault-Tolerant Prescribed Performance Control for Automatic Carrier Landing in Communication Environments Under Air-Wake Disturbances and Actuator Faults

Article References: Wu, Q., Zhu, Q., Wei, L., Wang, L., & Jiang, W. (2026). Robust Predefined-Time Fault-Tolerant Prescribed Performance Control for Automatic Carrier Landing in Communication Environments Under Air-Wake Disturbances and Actuator Faults. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01266-9

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01266-9

Keywords: automatic carrier landing, fault-tolerant control, predefined-time control, sliding mode control, prescribed performance, extended state observer, air-wake disturbance, actuator faults, Lyapunov stability, carrier-based aircraft, flight control systems, disturbance rejection